{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T17:56:22Z","timestamp":1775584582324,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,11,9]],"date-time":"2014-11-09T00:00:00Z","timestamp":1415491200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s11063-014-9397-y","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T15:03:10Z","timestamp":1415977390000},"page":"763-784","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":118,"title":["Finite-Time Stability and Its Application for Solving Time-Varying Sylvester Equation by Recurrent Neural Network"],"prefix":"10.1007","volume":"42","author":[{"given":"Yanjun","family":"Shen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Miao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuehua","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Shen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,9]]},"reference":[{"issue":"5","key":"9397_CR1","doi-asserted-by":"crossref","first-page":"1724","DOI":"10.1109\/TASL.2007.896669","volume":"15","author":"MD Skowronski","year":"2007","unstructured":"Skowronski MD, Harris JG (2007) Noise-robust automatic speech recognition using a predictive echo state network. IEEE Trans Audio Speech Lang Process 15(5):1724\u20131730","journal-title":"IEEE Trans Audio Speech Lang Process"},{"key":"9397_CR2","doi-asserted-by":"crossref","unstructured":"Burrows N, Niranjan M (1994) The use of recurrent neural networks for classification. In: IEEE workshop on neural networks for signal processing IV, Glasgow, pp 117\u2013125","DOI":"10.1109\/NNSP.1994.366057"},{"key":"9397_CR3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/S0925-2312(01)00706-8","volume":"50","author":"M Husken","year":"2003","unstructured":"Husken M, Stagge P (2003) Recurrent neural networks for time series classification. Neurocomputing 50:223\u2013235","journal-title":"Neurocomputing"},{"key":"9397_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2012.01.034","volume":"91","author":"S Li","year":"2012","unstructured":"Li S, Chen S, Liu B, Li Y, Liang Y (2012) Decentralized kinematic control of a class of collaborayive redundant manipulators via recurrent neural networks. Neurocomputing 91:1\u201310","journal-title":"Neurocomputing"},{"issue":"7","key":"9397_CR5","first-page":"4891","volume":"12","author":"S Lin","year":"2012","unstructured":"Lin S, Li Y, Liu B (2012) Model-free control of Lorenz chaos using an approximate optimal control strategy. Commun Nonlinear Sci Numer Simul 12(7):4891\u20134900","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"9397_CR6","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1287\/ijoc.11.1.15","volume":"11","author":"KA Smith","year":"1999","unstructured":"Smith KA (1999) Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J Comput 11:15\u201334","journal-title":"INFORMS J Comput"},{"key":"9397_CR7","unstructured":"Li S, Lou Y, Liu B (2012) Bluetooth aided mobile phone localization: a nonlinear neural circuit approach. ACM Trans Embed Comput Syst"},{"issue":"10","key":"9397_CR8","doi-asserted-by":"crossref","first-page":"3088","DOI":"10.1073\/pnas.81.10.3088","volume":"81","author":"JJ Hopfield","year":"1984","unstructured":"Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81(10):3088\u20133092","journal-title":"Proc Natl Acad Sci USA"},{"issue":"8","key":"9397_CR9","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1109\/TAC.2005.852558","volume":"50","author":"F Ding","year":"2005","unstructured":"Ding F, Chen T (2005) Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans Auto Control 50(8):1216\u20131221","journal-title":"IEEE Trans Auto Control"},{"key":"9397_CR10","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.cam.2008.06.014","volume":"224","author":"B Zhou","year":"2009","unstructured":"Zhou B, Li ZY, Duan GR, Wang Y (2009) Least squares solutions to general coupled Sylvester matrix equations. J Comput Appl Math 224:759\u2013776","journal-title":"J Comput Appl Math"},{"issue":"5","key":"9397_CR11","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1109\/TAC.1968.1098973","volume":"13","author":"R Manherz","year":"1968","unstructured":"Manherz R, Jordan B, Hakimi S (1968) Analog methods for computation of the generalized inverse. IEEE Trans Auto Control 13(5):582\u2013585","journal-title":"IEEE Trans Auto Control"},{"key":"9397_CR12","unstructured":"Jang JS, Lee SY, Shin SY (1987) An optimization network for matrix inversion. In: Proceedings of NIPS87, Graz, pp 397\u2013401"},{"issue":"6","key":"9397_CR13","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1109\/TNN.2005.857946","volume":"16","author":"Y Zhang","year":"2005","unstructured":"Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16(6):1477\u20131490","journal-title":"IEEE Trans Neural Netw"},{"issue":"10","key":"9397_CR14","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1109\/TNN.2011.2163318","volume":"22","author":"L Xiao","year":"2011","unstructured":"Xiao L, Zhang Y (2011) Zhang neural network versus gradient neural network for solving time-varying linear inequalities. IEEE Trans Neural Netw 22(10):1676\u20131684","journal-title":"IEEE Trans Neural Netw"},{"issue":"7","key":"9397_CR15","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1109\/TCSI.2008.2007065","volume":"56","author":"Y Zhang","year":"2009","unstructured":"Zhang Y, Ma W, Cai B (2009) From Zhang neural network to Newton iteration for matrix inversion. IEEE Trans Circuits Syst I 56(7):1405\u20131415","journal-title":"IEEE Trans Circuits Syst I"},{"key":"9397_CR16","volume-title":"Zhang neural networks & neural-dynamic method","author":"Y Zhang","year":"2011","unstructured":"Zhang Y, Yi C (2011) Zhang neural networks & neural-dynamic method. Nova Science Publishers Inc., New York"},{"key":"9397_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00521-010-0452-y","volume":"20","author":"Y Zhang","year":"2011","unstructured":"Zhang Y, Yi C, Guo D, Zheng J (2011) Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation. Neural Comput Appl 20:1\u20137","journal-title":"Neural Comput Appl"},{"key":"9397_CR18","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1145\/361573.361582","volume":"15","author":"RH Bartels","year":"1972","unstructured":"Bartels RH, Stewart GW (1972) Solution of the matrix equation $$AX + XB = C$$ A X + X B = C . Commun ACM 15:820\u2013826","journal-title":"Commun ACM"},{"key":"9397_CR19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s11063-012-9241-1","volume":"37","author":"S Li","year":"2013","unstructured":"Li S, Chen SF, Li B (2013) Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function. Neural Process Lett 37:189\u2013205","journal-title":"Neural Process Lett"},{"key":"9397_CR20","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1137\/S0363012997321358","volume":"38","author":"SP Bhat","year":"2000","unstructured":"Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38:751\u2013766","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"9397_CR21","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/00207721003770569","volume":"43","author":"YJ Shen","year":"2012","unstructured":"Shen YJ, Huang YH (2012) Global finite-time stabilisation for a class of nonlinear systems. Int J Syst Sci 43(1):73\u201378","journal-title":"Int J Syst Sci"},{"key":"9397_CR22","doi-asserted-by":"crossref","unstructured":"Wang WP, Peng HP, Li LX, Xiao JH, Yang YX (2013) Finite-time function projective synchronization in complex multi-links networks with time-varying delay. Neural Process Lett. doi: 10.1007\/s11063-013-9335-4","DOI":"10.1007\/s11063-013-9335-4"},{"key":"9397_CR23","volume-title":"Neuro-dynamic programming, optimization and neural computation series, 3","author":"DP Bertsekas","year":"1996","unstructured":"Bertsekas DP, Tsitsiklis JN (1996) Neuro-dynamic programming, optimization and neural computation series, 3. Athena Scientific, Belmont"},{"key":"9397_CR24","unstructured":"Kamruzzaman J, Aziz SM (2002) A note on activation function in multilayer feed forward learning. In: Proceedings of the 2002 international joint conference on neural networks 2002, IJCNN 02, vol 1, Honolulu, pp 519\u2013523"},{"key":"9397_CR25","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/41.184820","volume":"40","author":"WB Gao","year":"1993","unstructured":"Gao WB, Huang JC (1993) Variable structure control of nonlinear systems: a new approach. IEEE Trans Ind Electron 40:45\u201355","journal-title":"IEEE Trans Ind Electron"},{"key":"9397_CR26","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.neunet.2014.01.010","volume":"53","author":"WP Wang","year":"2014","unstructured":"Wang WP, Li LX, Peng HB, Xiao JH, Yang YX (2014) Synchronization control of memristor-based recurrent neural networks with perturbations. Neural Netw 53:8\u201314","journal-title":"Neural Netw"},{"key":"9397_CR27","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1140\/epjb\/e2013-30517-6","volume":"86","author":"LX Li","year":"2013","unstructured":"Li LX, Kurths Jrgen (2013) Exponentially asymptotic synchronization of uncertain complex time-delay dynamical networks. Eur Phys J B 86:125. doi: 10.1140\/epjb\/e2013-30517-6","journal-title":"Eur Phys J B"},{"key":"9397_CR28","volume-title":"Classical and modern regression with applications","author":"RH Myers","year":"1994","unstructured":"Myers RH (1994) Classical and modern regression with applications, 2nd edn. PWS-KENT Publishing Company, Boston","edition":"2"},{"key":"9397_CR29","volume-title":"Introduction to inverse kinematics with Jacobian transpose. Pseudo inverse and damped least squares methods. Technical Report","author":"SR Buss","year":"2004","unstructured":"Buss SR (2004) Introduction to inverse kinematics with Jacobian transpose. Pseudo inverse and damped least squares methods. Technical Report. University of California, San Diego"},{"key":"9397_CR30","volume-title":"Generalized inverses of linear transformations","author":"LC Stephen","year":"2009","unstructured":"Stephen LC, Carl DM (2009) Generalized inverses of linear transformations. Society for Industrial and Applied Mathematics, Philadephia"},{"issue":"1","key":"9397_CR31","first-page":"471","volume":"15","author":"KS Banerjee","year":"1980","unstructured":"Banerjee KS (1980) Generalized inverse of matrices and its applications. Technometrics 15(1):471\u2013512","journal-title":"Technometrics"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-014-9397-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-014-9397-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-014-9397-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T00:34:10Z","timestamp":1559349250000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-014-9397-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,9]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["9397"],"URL":"https:\/\/doi.org\/10.1007\/s11063-014-9397-y","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,9]]}}}